You will be paying $$8,200$ a year in tuition expenses at the end of the next two years. Bonds currently yield $9\%.$

Required:

What are the present value and duration of your obligation?

What maturity zero$-$coupon bond would immunize your obligation, give duration and face value?

Suppose you buy a zero$-$coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to $11\%.$ What happens to your net position, that is$,$ to the difference between the value of the bond and that of your tuition obligation and by what value does the position change?

by what value does the position change if rates fall immediately to $8\%?$